Newbie type question: Prime Numbers

[SHT]

Hi all,
I'm at the stage of learning and understanding Prime Numbers. A few players have some interesting theories on a number selection strategy for primes.

I'm not particularly interested in Prime numbers as a predictive tool but purely a filtering tool. Analysis shows that observed primes in the Canadian and UK 6/49 run close to the theoretical odds. Hence I am considering eliminating combinations that contain 5 and 6 primes= 0.77% of the population <combined odds>.

My problem is I keep thinking what's the big deal! I can't seriously be thinking about defining and filtering subgroups of a 6/49 lotto in terms of this integer attribute! My point is this, has anyone run a series of tests on randomly selected groups of 15 numbers. And compared the observed appearances in their 6/49 lotto to prime number appearances in each draw? (I know the theoretical odds are identical).

I would really love to know peoples opinions. Or has this discussion taken place before?

SHTH

 

[GillesD]

Prime numbers

SHT

I ran the test you were wondering about: selecting 15 random numbers and checking how many times each of these numbers appeared in each of the 2218 draws of Lotto 6/49. The bonus number was never considered.

The test was done 10 times and for each test, the first line gives the random numbers and the second line the number of times they appeared respectively 0 / 1 / 2 / 3 / 4 / 5 / 6 times

Test #1
16 - 12 - 42 - 04 - 17 - 43 - 32 - 44 - 08 - 39 - 10 - 02 - 06 - 21 - 33
221 -- 654 -- 783 -- 431 – 115 -- 14 -- 0
Test #2
48 - 01 - 27 - 44 - 38 - 45 - 18 - 12 - 23 - 10 - 13 - 40 - 39 - 09 - 03
216 -- 656 -- 762 -- 453 -- 123 -- 08 -- 0
Test #3
47 - 19 - 21 - 34 - 45 - 36 - 18 - 28 - 15 - 26 - 08 - 04 - 42 - 40 - 02
210 -- 655 -- 762 -- 454 -- 122 -- 15 -- 0
Test #4
15 - 43 - 07 - 02 - 32 - 30 - 38 - 25 - 28 - 11 - 09 - 35 - 23 - 29 - 19
233 -- 677 -- 741 -- 420 -- 130 -- 16 -- 1
Test #5
32 - 04 - 37 - 20 - 07 - 46 - 11 - 23 - 09 - 15 - 47 - 45 - 21 - 42 - 17
207 -- 666 -- 755 -- 459 -- 111 -- 18 -- 2
Test #6
19 - 41 - 35 - 04 - 25 - 17 - 11 - 18 - 02 - 23 - 32 - 39 - 06 - 33 - 07
255 -- 652 -- 759 -- 422 -- 113 -- 16 -- 1
Test #7
03 - 26 - 18 - 28 - 22 - 39 - 21 - 43 - 05 - 15 - 01 - 38 - 42 - 47 - 17
211 -- 658 -- 776 -- 448 -- 109 -- 16 -- 0
Test #8
45 - 21 - 41 - 11 - 34 - 32 - 35 - 10 - 31 - 04 - 05 - 06 - 19 - 48 - 14
225 -- 635 -- 783 -- 446 -- 109 -- 20 -- 0
Test #9
35 - 30 - 01 - 29 - 26 - 33 - 22 - 10 - 05 - 21 - 20 - 38 - 34 - 09 - 28
229 -- 663 -- 742 -- 446 -- 124 -- 14 -- 0
Test #10
20 - 46 - 27 - 16 - 34 - 07 - 08 - 09 - 33 - 19 - 15 - 48 - 32 - 43 - 14
213 -- 625 -- 783 -- 450 -- 133 – 12 -- 2

Overall here is a brief summary giving the number of times the 15 numbers appeared in all draws, then the expected value (rounded) the actual number of time in 2218 draws and finally the average, the minimum and the maximum for the 10 tests:

0 time: Exp: 213 -- Real: 203 -- Avg: 222.0 -- Min : 207-- Max : 255
1 time: Exp: 662 -- Real: 647 -- Avg: 654.1 -- Min : 625 -- Max : 677
2 times: Exp: 773 -- Real: 746 -- Avg: 764.6 -- Min : 741 -- Max : 783
3 times: Exp: 432 -- Real: 431 -- Avg: 442.9 -- Min : 420 -- Max : 459
4 times: Exp: 121 -- Real: 131 -- Avg: 118.9 -- Min : 109 -- Max : 133
5 times: Exp: 16 -- Real: 17 -- Avg: 14.9 -- Min : 08 -- Max : 20
6 times: Exp: 1 -- Real: 0 -- Avg: 0.6 -- Min : 0 -- Max : 2

So, there is not much difference and running the same test with different random numbers will produce similar but not identical results. You could run the same test with any set of 15 numbers (first 15 numbers, first 15 even numbers, last 15 multiple-of-3 numbers, etc.) and you would get similar results.

 

[SHT]

Cheers

Thanks GillesD for the data mining.

I suspected the results wouldn't be much different.

So in yours or anyones opinion, is it an absurd notion to eliminate combinations that contain 5 and 6 primes?. (NB I'm using all 49 numbers).

SHTH

 

[GillesD]

15-number sets

SHT

Elimination of numbers based on criteria that has nothing to do with lotteries is, in my opinion, a fun but meaningless exercise. Choose any set of fifteen numbers and the probability of finding from 0 to 6 of those numbers in the winning combination is exactly as you stated initially. Of course, the actual results for each set will differ and based on past results, it is possible to determine which 15 numbers would have perform best; or what could be called the quest for the optimum set.

Here is the performance of 6 sets of 15 numbers that are certainly not random but have a definite se-quence. The data is presented with first the 15 numbers, then the number of times they appeared re-spectively 0 / 1 / 2 / 3 / 4 / 5 / 6 times in the 2218 draws:

A – The first 15 numbers:
01-02-03-04-05-06-07-08-09-10-11-12-13-14-15: 242--674--773--381--117--012--001
B – The last 15 numbers:
35-36-37-38-39-40-41-42-43-44-45-46-47-48-49: 175--653--789--428--142--012--001
C - The first 15 even numbers:
02-04-06-08-10-12-14-16-18-20-22-24-26-28-30: 219--686--794--379--110--012--000
D – The last 15 numbers that are multiple of 3:
06-09-12-15-18-21-24-27-30-33-36-39-42-45-48: 218--680--748--431--110--012--001
E – Starting with 1, sequences of 3 consecutive numbers followed by a delta of 5:
01-02-03-08-09-10-15-16-17-22-23-24-29-30-31: 220--666--772--425--103--014--000
F – Starting with I, sequences of 3 numbers with a delta of 2 followed by a delta of 5:
01-03-05-10-12-14-19-21-23-28-30-32-37-39-41: 217--664--786--405--112--015--001

As a reminder, the expected values for 0 to 6 occurrences in the winning combination are respectively:
213 – 662 – 773 – 432 – 121 – 16 – 1

All values are fairly near the expected ones except the values for 0 occurrence of the first 15 numbers (242 vs 223) and of the 15 last numbers (175 vs 223). This confirms the slight bias in Lotto 6/49 toward higher numbers.